A biscuit jointer definitely won't do, and it doesn't need to be a jointer/planer combo. A plain benchtop or pedestal jointer will work fine.
This is a bench jointer:
This is a pedestal jointer:
Either of those will do the trick quite quickly. It is a type of planer, but it's not a thickness planer. It's purpose is to plane edges flat and smooth for gluing.
There are also handplane jointers, mostly known as #7 jointer and #8 jointer planes. I have a #8. It looks basically like this:
(The #7 is smaller, and is for little girls.)
It has the same purpose as the power jointers, but is obviously hand powered, and it takes a lot longer.
The thickness planer is just to take the lumber down to the thickness of the bass body. I like 1.5" thick bodies, so when I get 8/4 lumber, I plane it down to just a hair above that thickness and then glue the lumber pieces together to make a blank. Because I plane it to thickness before I glue the body blank up, I don't need a terribly wide planer. Mine has a 12.5" wide cutting capacity, which is too small for a glued blank or body to fit through. If you want like a 15" thickness planer so you can plane after gluing, you're going to be spending a lot of money for it.
So I take my raw lumber (7" x 41" piece of 8/4 whatever) and 1) plane it down to thickness, and then 2) cut it at 22" so that I can glue it into a blank, and then 3) joint both gluing edges, then 4) glue them together, and after the glue cures, I 5) scrape and sand the glue off to prepare for routing.
Buying a pre-made blank removes that work and the required tools from the process. I'd recommend it.